Thermalization & hydrodynamics in Bjorken & Gubser flows

TL;DR

This paper compares hydrodynamic models with exact solutions for expanding systems, revealing universal scaling in some quantities but limitations in entropy description due to non-hydrodynamic modes.

Contribution

It provides a detailed comparison of third-order Chapman-Enskog and anisotropic hydrodynamics against exact Boltzmann solutions in Bjorken and Gubser flows.

Findings

Normalized shear matches attractors with high accuracy.

Universal late-time scaling relations are observed for certain quantities.

Hydrodynamic models less accurately describe entropy evolution.

Abstract

The dynamical scaling behavior of hydrodynamic and non-hydrodynamic moments of the distribution function is studied using third-order Chapman-Enskog hydrodynamics and anisotropic hydrodynamics for systems undergoing Bjorken and Gubser expansions, where exact solutions of the Boltzmann equation in Relaxation Time Approximation (RTA) are available for comparison. While dimensionless quantities like normalized shear, pressure anisotropy and normalized entropy show at late times universal scaling relations with small (large) Knudsen number for Bjorken (Gubser) flows, dimensionful quantities like the entropy per unit rapidity do not. Although the two hydrodynamic approximation schemes describe the exact attractors for normalized shear with high accuracy, their description for the normalized entropy is less precise. We attribute this to non-negligible couplings to non-hydrodynamic modes in the entropy evolution.